Re: [seul-edu] [OT] summation of 1/2x

[Ray Olszewski <ray@comarre.com>]

You missed it, jm. The series is easy to sum from 1 to infinity, but
impossible to sum from 0 to infinity, since the starting term (1/0) is
undefined. I (and others, no doubt) assumed the original posting read 0 due
to a typo or a minor slip of the tongue (right, Brian?). Surely this typo is
all that Jan was alluding to (otherwise, why the smiley?).

And BTW, the sum (from 1 to infinity) is easy to calculate without cutting
pieces of paper. Set it equal to X, double it, and subtract the original
equation from the doubled one. All the terms cancel out except the leading
2. It's the basic "training wheels" exercise in how to sum an infinite
series that converges. In your variant (2 to infinity), the same approach
will cause all but the leading 1 to cancel out. 

And a technical distinction: in math, you can **illustrate** things by
cutting up bits of paper, but you cannot **prove** them that way.

At 04:25 PM 4/5/00 +0100, jm wrote:
>
>> > I got to thinking of this last week when a friend and I were trying to
>> > remember what the summation of 1/x evaluated from x=0 to x=infinity
>> > is.
>>
>>I would like to see what you found! ;-)
>
>If I remember well, there is a trick to calculate the sum of 1/2x from 1 to 
>infinity
>you just need a sheet of paper:
>  + first you cut in half the sheet of paper: you get 1/2 sheet and another 
>1/2 sheet
>  + then you cut in half again one of the 1/2 sheet: you get 1/4 and 1/4
>+  then you cut in half again...
>
>so you can prove that 1/2+1/4+1/8+..+1/2n+.. = 1

------------------------------------"Never tell me the odds!"---
Ray Olszewski                                        -- Han Solo
Palo Alto, CA           	 	         ray@comarre.com        
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